In this paper, we prove that, in dimension one, the Poincaré inequality is equivalent to a new transport-chi-square inequality linking the square of the quadratic Wasserstein distance with the chi-square pseudo-distance. We also check tensorization of this transport-chi-square inequality.

Large $H$-selfadjoint random matrices are considered. The matrix $H$ is assumed to have one negative eigenvalue, hence the matrix in question has precisely one  eigenvalue of nonpositive type. It is showed that this eigenvalue converges in probability to a deterministic…

It is well known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give a simple proof for this result, which generalizes to any continuous local martingale…

We provide a complete characterisation of the class of one-dimensional  time-homogeneous diffusions consistent with a given law at an exponentially distributed time using classical results in diffusion theory. To illustrate we characterise the class of diffusions with the same  distribution as…

This article proves an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries.

We give sharp estimate for the free energy of directed polymers in random environment in dimension 1+1. This estimate was known for a Gaussian environment, we extend it to the case where the law of the environment is infinitely divisible.

This is an erratum for paper "Convergence in law in the second Wiener/Wigner chaos" appeared in ECP volume 17 paper number 36.

Moments formulae for Wiener integrals of a subordinator with exponential moments are obtained in terms of the general Bell polynomials and the moments of the Lévy measure of this subordinator. We also express the Appell and Scheffer polynomials associated to…

In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., $p_c< p_u$. Furthermore, we show that percolation and self-avoiding walk on such graphs have mean-field critical exponents. In particular, the…

This is an erratum for paper "Concentration bounds for stochastic approximation" appeared in ECP volume 17 paper number 47.